I would like to find a free or paid service which will test my web application and declare whether it's secured or not. Is there such thing which is acceptable by the community or some corporate business units?
I want to know if there is such standard that gives a recognition that my web application is secured
There is no such "standard". There are various vendors offering services to check your site for vulnerabilities and then allow you to put some seal on the site to show that you've passed there checks. But, the quality of the checks they do is often very limited (depending on what you pay) which means that these seals should not really be trusted. Apart from that anybody can put an image of such a seal on their site even if the site was never checked or just invent their own trust seal to make the site look more trustable.
If you really want to make sure that your site is mostly secure hire a penetration tester with a good reputation, give him enough time, money and information to analyze your site and follow his advice in securing the site. Better yet, get the help of such testers and security consultants already in the design phase of your web application so that your developers are aware of the problems and build the security into the design of the application instead of trying to add security on top of an inherent insecure application later.